In this paper, we propose an R package, called RKHSMetaMod, that implements a procedure for estimating a meta-model of a complex model. The meta-model approximates the Hoeffding decomposition of the complex model and allows us to perform sensitivity analysis on it. It belongs to a reproducing kernel Hilbert space that is constructed as a direct sum of Hilbert spaces. The estimator of the meta-model is the solution of a penalized empirical least-squares minimization with the sum of the Hilbert norm and the empirical $L^2$-norm. This procedure, called RKHS ridge group sparse, allows both to select and estimate the terms in the Hoeffding decomposition, and therefore, to select and estimate the Sobol indices that are non-zero. The RKHSMetaMod package provides an interface from R statistical computing environment to the C++ libraries Eigen and GSL. In order to speed up the execution time and optimize the storage memory, except for a function that is written in R, all of the functions of this package are written using the efficient C++ libraries through RcppEigen and RcppGSL packages. These functions are then interfaced in the R environment in order to propose a user-friendly package.
翻译:在本文中,我们提出一个名为 RKHSMetataMod 的R 软件包,用于对复杂模型的元模型进行估算。 元模型的元模型接近复杂模型的Hoffing分解, 并允许我们对其进行敏感度分析。 它属于作为希尔伯特空间的直接和与Hilbert空间的直接和建造的复制核心Hilbert空间。 元模型的估算器是用希尔伯特规范与实证价值$L2$- 诺尔姆之和来进行惩罚性最低经验水平最小值最小值的解决方案。 这个程序叫做 RKHS 脊层群, 允许选择和估计该复杂模型的分解条件, 并允许我们对其进行敏感度分析。 它属于作为Hilbert 空间的直接和 希尔伯特 空间之和 。 元模型的估算器是C+ 图书馆 Eigen 和 GS 的连接器。 为了加快执行时间并优化存储记忆, 除了在R 中写入的功能之外, 这个软件包的所有功能都是用高效的 C++ 软件包的 Rpp 和 Rpp 的 Rpp 系统 的用户环境 。